Problem: Simplify the following expression: $q = \dfrac{x + 10}{5x + 10} - \dfrac{3x + 19}{5x + 10}$
Solution: Since the expressions have the same denominator we simply subtract the numerators: $q = \dfrac{x + 10 - (3x + 19)}{5x + 10}$ Distribute the negative sign: $q = \dfrac{x + 10 - 3x - 19}{5x + 10}$ Combine like terms: $q = \dfrac{-2x - 9}{5x + 10}$